Existence analysis of a single-phase flow mixture with van der Waals pressure

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F18%3A00319358" target="_blank" >RIV/68407700:21340/18:00319358 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1137/16M1107024" target="_blank" >http://dx.doi.org/10.1137/16M1107024</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1137/16M1107024" target="_blank" >10.1137/16M1107024</a>

Result language
angličtina
Original language name
Existence analysis of a single-phase flow mixture with van der Waals pressure
Original language description
The transport of single-phase fluid mixtures in porous media is described by cross- diffusion equations for the mass densities. The equations are obtained in a thermodynamic consistent way from mass balance, Darcy’s law, and the van der Waals equation of state for mixtures. The model consists of parabolic equations with cross diffusion with a hypocoercive diffusion operator. The global-in-time existence of weak solutions in a bounded domain with equilibrium boundary conditions is proved, extending the boundedness-by-entropy method. Based on the free energy inequality, the large-time convergence of the solution to the constant equilibrium mass density is shown. For the two-species model and specific diffusion matrices, an integral inequality is proved, which reveals a minimum principle for the mass fractions. Without mass diffusion, the two-dimensional pressure is shown to converge exponentially fast to a constant. Numerical examples in one space dimension illustrate this convergence.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics

Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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